Question

Using complete square to slove for x in the equation (x+7) (x-9)=25

Answer 1

Answer:

$x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}$

Step-by-step explanation:

Apply Distributive property:

$(x+7)(x-9)=25\\\\x^2-9x+7x-63=25$

Add like terms and then add 63 to both sides of the equation:

$x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88$

Pick the coefficient of the x term, divide it by 2 and square it:

$(\frac{2}{2})^2=1$

Add it to both sides of the equation:

$x^2-2x+1=88+1$

Rewriting the left side as a squared binomial, we get:

$(x-1)^2=89$

Apply square root to both sides:

$\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}$

And finally we need to add 1 to both sides of the equation. Then we get:

$x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}$